"The era of strategic patience with the North Korean regime has failed," Trump said in a statement from the Rose Garden. "And, frankly, that patience is over."
The remarks were the latest sign that Trump is growing increasingly frustrated
with the lack of progress in curbing North Korea's nuclear and ballistic missile programs, which top US officials have eyed with increasing concern in recent months.
The South Korean President's visit to the White House came after Trump approved a series of measures designed to ratchet up pressure on North Korea -- while also sending signals to China about the US' shrinking patience.
The Treasury Department on Thursday imposed new sanctions on a Chinese bank and several Chinese nationals
while the State Department approved a $1 billion arms deal with Taiwan
. Both moves appeared aimed at unsettling China, which the US has repeatedly urged to pressure North Korea into changing its behavior, with little success.
Trump on Friday warned that the US is facing "the threat of the reckless and brutal regime in North Korea" that "has no regard for the safety and security of its people or its neighbors" and vowed the US would continue to act to defend US interests and allies in the region.
Moon, who was elected on a platform of increased engagement with North Korea, also warned that "threats and provocations from the North will be met with a stern response" and vowed South Korea and the US will "strengthen" their joint deterrence capabilities.
But he also urged the North Korean regime "to promptly return to the negotiating table" to achieve a peaceful end to its nuclear program.
Beyond its ongoing nuclear and ballistic missile activity, the sense of alarm in the US has also grown after American student Otto Warmbier fell into a coma while in North Korean custody and died days after he was returned to the US.
"The North Korean dictatorship has no regard for the safety and security of its people or its neighbors and has no respect for human life -- and that's been proven over and over again," Trump said, before also thanking Moon for expressing his condolences over Warmbier's death.
The two men did not take questions, marking the second consecutive foreign visit where Trump has not taken questions alongside a world leader he is hosting at the White House.
Moon first arrived at the White House Thursday night where he and his wife dined with Trump and the US first lady.
Moon returned to the White House on Friday morning for a series of meetings after first laying a wreath at the Korean War memorial with Vice President Mike Pence.
Trump and Moon's discussions went beyond ways to confront the North Korean regime, also centering on the trading relationship between the US and South Korea, following Trump's criticism of the bilateral free trade deal between the two countries, which Trump has called a bad deal for the US.
"We are renegotiating a trade deal right now as we speak with South Korea and hopefully it will an equitable deal, a fair deal to both parties," Trump said as he greeted Moon in the Oval Office on Friday morning. "It's been a rough deal for the United States but I think that it will be much different for the United States."
Trump added in the Rose Garden that he was "encouraged by President Moon's assurances that he will work to create a level playing field so that American workers and businesses and especially automakers can have a fair shake at dealing with South Korea."
But even on trade, China appeared to be at the forefront of the administration's mind.
In remarks during the bilateral meeting between the US and South Korean sides, National Economic Director Gary Cohn knocked China's "predatory practices" on trade and said the Trump administration hopes to partner with South Korea to jointly tackle Chinese trade abuses that impact both countries.